Monday, April 14, 2014

Why (n-1)?

My first day in my office in
Albany, I made a point of introducing myself to Leslie T. Wilkins.Shortly thereafter, Les invited me to team
teach a seminar in one of the school of crimjus’s core areas: Philosophical
Issues of Law and Social Control.He
proposed over lunch that we invite another philosopher from the
university.He first picked Stefan
Temesvary, one of only several members of the Astronomy Department (later
abolished entirely by a colleague who led the university “task force” in making
the decision, as he explained to me at yet another lunch meeting).Stefan had been forced as a draftee German physicist
to develop the V-2 rocket at Peenemunde that was to rain bombs on London; he
described watching a rocket “…go up…., and then it came down” with an ironic
grin.Next came Jim McClelland, a
philosopher in the Historical and Philosophical Foundations of Education in
which my wife Jill received her Sociology Ph.D.I vividly Jim using his inaugural lecture in our seminar to fill 2
blackboards with symbolic logic as “proof” that only anarchism works.That seminar remains the highlight of my
teaching experiences.Les, Barb, Jill
and I became close friends, and visited them twice in England after Les’s retirement.I dedicated my 1980 book, Crime Control Strategies, a systems
analysis of what it meant when each major measure of crime and criminality,
from convictions of crime, through arrests and self-reports, on through
measures of criminality down to “recidivism.”

Les mentored me personally and
enthusiastically (often as I sat with him after hours in his living room)
throughout our times together.One thing
he pointed out to me was that regression models simply made analyses of
variance ordinal rather than descriptive.And regression was indeed what he brought to his collaboration with Don
Gottfredson to create the statistical system that became the first U.S. federal
parole guidelines, which as I predicted to Les, soon became perverted into the
notorious federal sentencing guidelines, to justify further incarceration
rather than to promote safe and early release from prison.

What struck me as most peculiar
about analyses of variance was that the numerator was not simply divided by the
total number of cases, but by (n-1).I
accepted implicitly that as Les said, that any 1 case in itself had no
variance, and so “n” by itself had no variance, and Les’s insistence that you
had to have at least 3 cases to have enough variation to infer variance, but it
is only as I write today that I think I can see why, in Euclidean geometric
terms.

In purely mathematical material
terms, 1 case equals a dot, a location that has purely unique significance in
itself, or in plain English, doesn’t matter at all, or in scientific terms, has
no significance.You have to place one
dot in relation to a second dot in order to show what direction they are
headed.You have to have three dots for
them together in the “third” dimension in order for them as a group to have any
substance at all in common.And you have
to move the three dots toward a fourth in order to show any movement of any
substance, the “fourth” dimension commonly known as “time.”

In social science, dots are
called “variables.”I learned in chapter
2 of my grad statistics text that it is a “fallacy” to “affirm a null
hypothesis.”Suppose we compare a group
of people who have never been convicted of a felony, say murder, and find that
the people who are black in one population have on average murdered more people
than the people who are white.Individually, the fact that someone happens to be black or white is
insignificant—the variable black or white is fixed for each individual who
happens to be black or white; it only signifies anything when it is some
average of 3 blacks and 3 whites; in itself, the fact that blacks “commit” more
“murders” than whites doesn’t even tell you anything but which group of any 3
blacks versus group of 3 whites is more likely include someone convicted of
murder.As for comparing 2 blacks to 2
whites, the odds of any single white or black being among all those convicted
of murder is simply fifty-fifty.The
odds of any single black or white person being convicted of murder in my “violent”
country are less than one in ten thousand, period.

My fellow criminologists, please
refrain from thinking you know anything about how dangerous or crime-free any
individual is by statistical profile.If
this be your “best evidence” of what to expect from any human being you have no
firsthand knowledge of, you know nothing.Love and peace--hal

About Me

I retired Jan. 2009 from after 33 years on the criminal justice faculty at Indiana University, Bloomington. I continue not to charge for any form of public service, including speaking and consulting, and now have plenty of free time to do so on request. I do not do social networking. I regularly monitor just one email account: pepinsky@indiana.edu; my home phone number is 1-614-885-6341; my skype name is halpep. My papers and such are archived at http://webapp1.dlib.indiana.edu/findingaids/view?brand=general&docId=InU-Ar-VAA9639.xml&doc.view=entire_text.
I am known as a co-founder of "peacemaking criminology." Page proofs of my latest, 2006 U of Ottawa Press book, Peacemaking: Reflections of a Radical Criminologist, are freely available at http://critcrim.org/sites/default/files/Pepinsky_proofs_0.pdf , the end of which lists my publications, nine books and over 80 articles and chapters in all, on a wide range of subjects from the international to the interpersonal level. My preceding book, A Criminologist's Quest for Peace, is also freely available at http://critcrim.org/pepinsky, and a pdf of Myths That Cause Crime is on the critcrim.org home page.